---
slug: /plat/trees
title: "Trees"
author: Benjamin Qi
order: 1
prerequisites: 
 - 
     - Silver - Depth First Search
---

Lowest Common Ancestor and other tree topics.

<!-- END DESCRIPTION -->

## Tree Diameter

### Tutorial

 - CPH 14.2

### Problems

 - [USACO Plat Newbarns](http://www.usaco.org/index.php?page=viewproblem2&cpid=817)
   - Copy of [Brain Network "Hard"](https://codeforces.com/contest/690/problem/C3)
 - [Tree Construction](https://csacademy.com/contest/archive/task/tree-construct)

## Lowest Common Ancestor

### Tutorial

 - CPH 18
 - [cp-algorithms: Lowest Common Ancestor](https://cp-algorithms.com/)

### Problems

USACO:

 - [USACO Plat Max Flow](http://www.usaco.org/index.php?page=viewproblem2&cpid=576)
 - [USACO Gold Milk Visits](http://www.usaco.org/index.php?page=viewproblem2&cpid=970)
 - [USACO Gold Cow Land](http://www.usaco.org/index.php?page=viewproblem2&cpid=921)
   - LCA + BIT
 - [USACO Plat Promote](http://www.usaco.org/index.php?page=viewproblem2&cpid=696)
   - Subtree + BIT
 - [USACO Plat Disrupt](http://www.usaco.org/index.php?page=viewproblem2&cpid=842)
   - HLD is possible, but just do binary jumps
 - [USACO Plat Tree Boxes](http://www.usaco.org/index.php?page=viewproblem2&cpid=948)
   - interactive!!
 - [USACO Plat Gathering](http://www.usaco.org/index.php?page=viewproblem2&cpid=866)
 - [USACO Plat Exercise](http://www.usaco.org/index.php?page=viewproblem2&cpid=901)
   - tricky

Other:

 - [Hot & Cold](https://dmoj.ca/problem/bts17p7) [](105)
 - [Root LCA Queries](https://csacademy.com/contest/archive/task/root-lca-queries/) [](107)

## Centroid Decomposition

### Tutorial

 - [GeeksForGeeks](http://www.geeksforgeeks.org/centroid-decomposition-of-tree/)
 - [Carpanese](https://medium.com/carpanese/an-illustrated-introduction-to-centroid-decomposition-8c1989d53308)

### Problems

 - [USACO Plat - At Large](http://www.usaco.org/index.php?page=viewproblem2&cpid=793)
   - very tricky
 - [DMOJ Bob Equilibrium](https://dmoj.ca/problem/dmopc19c7p6)

## Heavy-Light Decomposition

 - probably not intended solution, but can help (ex. for "Disrupt")

### Tutorial

 - [Anudeep2011](https://blog.anudeep2011.com/heavy-light-decomposition/)
 - [AI-Cash](http://codeforces.com/blog/entry/22072)
 - [adamant](https://codeforces.com/blog/entry/53170)

### Problems

??

## Small to Large (Offline)

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